Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider the given function. f(x) = e2x-4 To determine the inverse of the given function, change f(x) to y, switch

and y, and solve for

Answer 1

Put them in this order in the fill in the blanks, X,Y, 4, 2

Explanation:

Answer 2

To determine the inverse of the given function, change f(x) to y, switch x and y and solve for y and
`f^(-1)(x)= (ln\ x+4)/(2)`

Explanation:

Data provided in the question

f(x) = e^2x - 4

Now

to find the inverse let

So,

y = e^2x - 4

Now

Replace x and y

Therefore

x = e^2y - 4

Now compute the value of y

So,

x + 4 = e^2y

Now take ln on both sides:

The equation is

ln(x+4) = ln(e^2y)

ln(x+4) = 2y

y = ln(x+4) ÷ 2

`f^(-1)(x)= (ln\ x+4)/(2)`

Therefore, To determine the inverse of the given function, change f(x) to y, switch x and y and solve for y and
`f^(-1)(x)= (ln\ x+4)/(2)`